Minimal Separating Sequences for All Pairs of States

14 Mar 2016Rick Smetsers, Joshua Moerman and David N. Jansen

Abstract

Finding minimal separating sequences for all pairs of inequivalent states in a
finite state machine is a classic problem in automata theory. Sets of minimal
separating sequences, for instance, play a central role in many conformance
testing methods. Moore has already outlined a partition refinement algorithm
that constructs such a set of sequences in O(mn) time, where m is the number of
transitions and n is the number of states. In this paper, we present an improved
algorithm based on the minimization algorithm of Hopcroft that runs in O(m log
n) time. The efficiency of our algorithm is empirically verified and compared to
the traditional algorithm.